1、統(tǒng)計(jì)運(yùn)用及品管實(shí)務(wù)工具,資料數(shù)據(jù) 基礎(chǔ)統(tǒng)計(jì)運(yùn)用概念 生產(chǎn)製造環(huán)境 實(shí)用品質(zhì)統(tǒng)計(jì)工具 製程能力分析與SPC統(tǒng)計(jì)製程控制,資料及數(shù)據(jù),你想瞭解什麼?,資訊源:,分組,離散型,名義型,順序型,間距型,“資料本身並不能提供資訊 必須對(duì)資料加以處理以後才能得到資訊, 而處理資料的工具就是統(tǒng)計(jì)學(xué)”.,衡量,連續(xù)型,比率型, 文字的 (A to Z) 圖示的 口頭的 數(shù)位的 (0-9),數(shù)據(jù),FAIL,PASS,數(shù)量 單價(jià) 說(shuō)明 總價(jià) 1$10.00$10.00 3$1.50$4.50 10$10.00$10.00 2$5.00$10.00,裝貨單,離散型資料和連續(xù)型資料,電氣電路,溫度,溫度計(jì),連續(xù)型,離

2、散型,卡尺,錯(cuò)誤,離散型資料 (通常) 分組 / 分類(lèi) 是 /否, 合格 / 不合格 不能計(jì)算 離散型資料 分級(jí) 很少用 很難加以計(jì)算 連續(xù)型資料 最常見(jiàn)的尺規(guī) 計(jì)算時(shí)要很小心 連續(xù)型資料 比例關(guān)係 可應(yīng)用演算法的多數(shù)公式,分類(lèi) 標(biāo)簽 第一、第二、第三 相對(duì)高度 字母順序 1234 溫度計(jì) 刻度盤(pán) 速度= 距離/時(shí)間 直尺,衡量工具分類(lèi),說(shuō)明,例子,衡量工具分類(lèi),名義型:不相關(guān)類(lèi), 只代表符合條件或不符合條件個(gè)體數(shù). 順序型:順序類(lèi),但沒(méi)有各類(lèi)間隔的資訊. 間距型:順序類(lèi),兩類(lèi)之間間隔相等,但沒(méi)有絕對(duì)零點(diǎn). 比例型:順序類(lèi),兩 類(lèi)之間間隔相等, 同時(shí)存在絕對(duì)零點(diǎn). .,離 散 型,連 續(xù) 型,

3、$,$,連續(xù)資料的優(yōu)勢(shì),連續(xù)的,離散的,信息量少,信息量多,基礎(chǔ)統(tǒng)計(jì)運(yùn)用概念,變異(Variation),當(dāng)我們從一過(guò)程中收集數(shù)據(jù),會(huì)發(fā)現(xiàn)數(shù)據(jù)不會(huì)永遠(yuǎn)相同,因?yàn)樽儺?Variation)在過(guò)程中隨時(shí)存在,變異(Variation),我們觀察到的變異,是在過(guò)程中各種擾動(dòng)累積起來(lái)的.,變異(Variation),參數(shù),X,X,X,X,X,X,X,X,X,量測(cè)值,分佈,多數(shù)在此,少數(shù)在此,Center均值,Spread散佈,雖然變異是隨機(jī)的,但他們的隨機(jī)性通常有模式存在,這種模式可用統(tǒng)計(jì)上的分佈(Distribution)來(lái)形容.如此變異加以統(tǒng)計(jì)分析,便可有某種程度的預(yù)測(cè)性存在並易於被理解或控制.,

4、變異(Variation),中心Center: 數(shù)據(jù)最集中在何處? 散佈Spread:數(shù)據(jù)變異程度及分散狀況如何? 形狀Shape:分佈是否對(duì)稱(chēng)?扁平?凹凸? 是否有異常區(qū),描述分佈(Distribution),變異(Variation),變異可以是穩(wěn)定(Stable)或不穩(wěn)定(Unstable)的. - 穩(wěn)定變異:變化的分佈較具預(yù)測(cè)性及一致性,對(duì)時(shí)間而言具可預(yù)測(cè)性 - 不穩(wěn)定變異:對(duì)時(shí)間而言不具可預(yù)測(cè)性,PROCESS #1 - Stable Variation穩(wěn)定,Part,T h i c k n e s s,PROCESS #2 - Unstable Variation不穩(wěn)定,Part,

5、Distribution,Distribution,T h i c k n e s s,變異(Variation),在製造過(guò)程中,有變異都是不好.問(wèn)題是我們能容忍到何種範(fàn)圍.我們能容忍的變異是具有以下兩項(xiàng)特徵:,STABLE (i.e., consistent and predictable over time).,CAPABLE (i.e., small variation compared to the product specifications.),Product Specifications,Parameter Distribution,穩(wěn)定,散佈小,控制變異(Variation),

6、瞭解過(guò)程:,使制程更好:,保持穩(wěn)定並維持高制程能力,過(guò)程由時(shí)間來(lái)看是否穩(wěn)? 制程能力是否能滿足目標(biāo)規(guī)格?,確認(rèn)並除去不穩(wěn)定原因 確認(rèn)並降低變異程度使?jié)M足規(guī)格,持續(xù)監(jiān)視及控制過(guò)程的變異源,特徵化,改善,控制,因?yàn)橛贸闃咏y(tǒng)計(jì),其結(jié)果只是估計(jì), 和真實(shí)可能有差異. 適當(dāng)?shù)某闃涌墒菇y(tǒng)計(jì)分析更準(zhǔn)確.,Statistics 分佈的數(shù)學(xué)描述與定義,中心Center: 數(shù)據(jù)最集中在何處? 散佈Spread:數(shù)據(jù)變異程度及分散狀況如何? 形狀Shape:分佈是否對(duì)稱(chēng)?扁平?凹凸? 是否有異常區(qū),樣本均值,=,X,樣本,抽樣概念-母體參數(shù)和樣本統(tǒng)計(jì)量,母體: 包含所關(guān)心特性的已經(jīng)製造或?qū)⒁u造的物件 的全體 樣本

7、: 在統(tǒng)計(jì)研究中實(shí)際測(cè)量的物件組。 樣本通常爲(wèi)所關(guān)心母體的子集,“母體參數(shù)”,“樣本統(tǒng)計(jì)量”,m = 母體均值,s = 樣本標(biāo)準(zhǔn)偏差,母體,s = 母體標(biāo)準(zhǔn)偏差,抽樣方法,抽樣方法 上面介紹了幾種從母體中抽樣的方式 隨機(jī)性-從母體中抽取的樣本設(shè)計(jì)應(yīng)使母體中每一個(gè)都有同等機(jī)會(huì)抽中. 代表性-作為同一母體中其他樣本的實(shí)例.,系統(tǒng)隨機(jī)抽樣,分組抽樣,每一小時(shí)在該點(diǎn) 抽3個(gè)樣本,隨機(jī)抽樣,每個(gè)均有被選上的相等機(jī)會(huì),層別式抽樣,母體被“層別”成幾個(gè)組,在每個(gè)組內(nèi)隨機(jī)選擇.,行進(jìn)中的過(guò)程,每隔n個(gè)柚樣,一般準(zhǔn)則,計(jì)數(shù)數(shù)據(jù):50-100 計(jì)量數(shù)據(jù):每個(gè)分組最少是30,均值: 一組值的算術(shù)平均均值: - 反映

8、所有值的影響 - 受極值影響嚴(yán)重 中位數(shù): 反應(yīng) 50% 的序一組數(shù)排序後居中的數(shù) - 在計(jì)算中不必包含所有值 - 相對(duì)於極值具有 “可靠性” 眾數(shù)值: - 在一組資料中最常發(fā)生的值,Median,(Mean平均),(Median中數(shù)),眾數(shù),Center(中心),50%,50%,全距: 在一組資料中，最高值和最低值 間的數(shù)值距離 變異 (s2): 每個(gè)資料點(diǎn)與均值的平均平方偏差 標(biāo)準(zhǔn)偏差 (s): 變異數(shù)的平方根. 量化變動(dòng)最常用的量,全距最大值最小值,Spread(散佈),The Rule states how and can be used to describe the entire

9、distribution: Roughly 60-75% of the data are within 1 of . Roughly 90-98% of the data are within 2 of . Roughly 99-100% of the data are within 3 of .,60-75%,90-98%,99-100%,m,m - s,m - 2 s,m + s,m + 2 s,m + 3 s,m - 3 s,Spread(散佈),The shape of a distribution can be described by skewness 歪斜 (denoted by

10、 1) and by kurtosis凹凸平坦 (denoted by 2).,歪斜,凹凸平坦,Shape (形狀),母體均值,樣本均值,母體標(biāo)準(zhǔn)偏差,樣本標(biāo)準(zhǔn)偏差,常用計(jì)算公式,母體變異,樣本變異,The most important and useful distribution shape is called the Normal distribution, which is symmetric(對(duì)稱(chēng)), uni-modal(單峰), and free of outliers (沒(méi)有特異點(diǎn)):,Normal Distribution常態(tài)分佈,“常態(tài)” 分佈是具有某些一致屬性的資料的分佈

11、這些屬性對(duì)理解基礎(chǔ)過(guò)程（資料從該過(guò)程中收集）的特徵非常有用. 大多數(shù)自然現(xiàn)象和人爲(wèi)過(guò)程都符合常態(tài)分配，可以用常態(tài)分配表示, 故大部份統(tǒng)計(jì)都假設(shè)是常態(tài)分佈。 即使在資料不完全符合常態(tài)分配時(shí)，分析結(jié)果也很接近。 特別不正常的分佈若假設(shè)為常態(tài)而去分析則有可能得到誤導(dǎo)結(jié)果。 有數(shù)學(xué)技術(shù)可將其轉(zhuǎn)變成常態(tài)分佈來(lái)作分析。,A Normal probability plot is a cumulative distribution plot where the vertical scale is changed in such a way that data from a Normal distributio

12、n will form a straight line:,Histogram,Cumulative Distribution,Normal Probability Plot,常態(tài)概率圖,Normal Distribution常態(tài)分佈,第一個(gè)屬性: 只要知道下面兩項(xiàng)就可以完全描述常態(tài)分配: 均值 標(biāo)準(zhǔn)差,常態(tài)分配的好處 -簡(jiǎn)化,第一個(gè)分佈,第二個(gè)分佈,第三個(gè)分佈,這三個(gè)分佈有什麼不同?,常態(tài)曲線和其概率,4,3,2,1,0,-,1,-,2,-,3,-,4,40%,30%,20%,10%,0%,99.73%,第二個(gè)屬性: 曲線下方的面積可以用於估計(jì)某“事件”發(fā)生的累積概率,95%,68%,樣本值的

13、概率,距離均值的標(biāo)準(zhǔn)偏差數(shù),得到兩值之間的值的累積概率,常態(tài)概率圖,我們可以用常態(tài)概率圖檢驗(yàn)一組給定的資料是否可以描述爲(wèi)“常態(tài)” 如果一個(gè)分佈接近常態(tài)分配，則常態(tài)概率圖將爲(wèi)一條直線。,資料收集時(shí)的重點(diǎn),How the data are collected affects the statistical appropriateness and analysis of a data set(資料如何收集可影響統(tǒng)計(jì)的適切性). Conclusions from properly collected data can be applied more generally to the process a

14、nd output. Inappropriately collected data CANNOT be used to draw valid conclusions about a process. Some aspects of proper data collection that must be accounted for are: The manufacturing environment(製程環(huán)境)from which the data are collected. When products are manufactured in batches or lots, the data

15、 must be collected from several batches or lots. Randomization(隨機(jī)). When the data collection is not randomized, statistical analysis may lead to faulty conclusions.,Continuous Manufacturing (連續(xù))occurs when an operation is performed on one unit of product at a time. An assembly line is typical of a c

16、ontinuous manufacturing environment, where each unit of product is worked on individually and a continuous stream of finished products roll off the line. The automotive industry is one example of Continuous Manufacturing. Other examples of continuously manufactured product are: television sets, fast

17、 food hamburgers, computers.,Lot/Batch Manufacturing (批次) occurs occurs when operations are performed on products in batches, groups, or lots. The final product comes off the line in lots, instead of a stream of individual parts. Product within the same lot are processed together, and receive the sa

18、me treatment while in-process. Lot/Batch Manufacturing is typical of the semiconductor industry and many of its suppliers. Other examples of lot/batch manufactured product include: chemicals, semiconductor packages, cookies.,生產(chǎn)製造環(huán)境,In Continuous Manufacturing the most important variation is between

19、parts In Lot/Batch Manufacturing, the variation can occur between the parts in a lot and between the lots: Product within the same lot is manufactured together. Product from different lots are manufactured separately. Because of this, each lot has a different distribution. This is important because

20、Continuous Manufacturing is a basic assumption for many of the standard statistical methods found in most textbooks or QC handbooks. These methods are not appropriate for Lot/Batch Manufacturing. Different statistical methods need to be used to take into account the several sources of variation in L

21、ot/Batch Manufacturing. 要注意: 連續(xù)和批量生產(chǎn)所用的統(tǒng)計(jì)方法有些不同,With Lot/Batch Manufacturing, each lot has a different mean. Due to random processing fluctuations, these lots will vary even though the process may be stable. This results in several “l(fā)evels” of distributions, each level with its own variance and mean

22、: A distribution of units of product within the same lot. A distribution of the means of different lots. The total distribution of all units of product across all lots.,2,2,2,2,2,2,2,X,1,2,X,2,2,1,2,1,2,1,;,X,;,X,;,X,X,X,X,+,=,+,=,=,=,=,總,總,總,6原則,變異數(shù)可相加, 標(biāo)準(zhǔn)差則不能相加 輸入變數(shù)變異數(shù)相加計(jì)算輸出中的總變異數(shù),所以,那麼,引起的變異數(shù),輸入變

23、數(shù),引起的變異數(shù),輸入變數(shù),過(guò)程輸出的變異數(shù),如果,process has small within-lot variation and large lot-to-lot variation (which is very common), data values from the same lot will be highly correlated, while data from different lots will be independent:,實(shí)用品質(zhì)統(tǒng)計(jì)工具,直方圖(Histograms) 柏拉圖(Pareto Diagrams) 散佈圖(Scatterplots) 趨勢(shì)圖(Tre

24、nd Charts),品質(zhì)統(tǒng)計(jì)圖表 -直方圖(Histograms),Histograms provide a visual description of the distribution of a set of data. A histogram should be used in conjunction with summary statistics such as and s. A histogram can be used to: Display the distribution of the data(現(xiàn)示數(shù)據(jù)的分佈). Provide a graphical indication

25、of the center, spread, and shape of the data distribution (較定性地顯示數(shù)據(jù)的均值,散佈及形狀). Clarify any numerical summary statistics (which sometimes obscure information). (顯示較模糊的統(tǒng)計(jì)結(jié)果). Look for outliers - data points that do not fit the distribution of the rest of the data. (顯示異常點(diǎn)),: : . . . : . . : : :.: : . :

26、 . : . .:.:.:.:.:.: : . -+-+-+-+-+-加侖/分鐘 49.00 49.50 50.00 50.50 51.00,點(diǎn)圖分佈,設(shè)想有一個(gè)泵流量爲(wèi)50加侖/分鐘的計(jì)量泵。 按照節(jié)拍對(duì)泵的實(shí)際流量進(jìn)行了100次獨(dú)立測(cè)量。 畫(huà)出各個(gè)點(diǎn)，每點(diǎn)代表一個(gè)給定值的輸出“事件”。當(dāng)點(diǎn)聚集起來(lái)時(shí)，泵的實(shí)際性能狀況可以看作泵流量的“分佈”。,5,1,.,3,5,0,.,8,5,0,.,3,4,9,.,8,4,9,.,3,4,8,.,8,4,0,3,0,2,0,1,0,0,直方圖分佈,還是這些資料，現(xiàn)在設(shè)想將其分組後歸入“區(qū)間”。泵流量點(diǎn)落入指定區(qū)間的次數(shù)決定區(qū)間條的高度。,頻率,加侖/分

27、鐘,品質(zhì)統(tǒng)計(jì)圖表 -直方圖(Histograms),品質(zhì)統(tǒng)計(jì)圖表 -直方圖(Histograms), Multi-Modal Shape(雙峰):, Skewed Shape(偏一邊): Data can be right-skewed or left-skewed. This data is right-skewed the right tail is longer than the left tail.,Outliers:特異點(diǎn),品質(zhì)統(tǒng)計(jì)圖表 -柏拉圖(Pareto Diagrams),While histograms are used to display the distributio

28、n of a set of continuous (measured) data, Pareto diagrams are used to display the distribution of discrete (counted) data, such as different types of defects. Pareto diagrams can also be used with continuous (measured) data, particularly in displaying variance components analysis results, as we will

29、 see later in this course. Pareto diagrams are a useful tool for determining which problems or types of problems are most severe or occur most frequently, hence should be given high priority for process improvement efforts. Pareto diagrams separate the significant vital few problems from the trivial

30、 many to help determine which problems to address first (and which to address later). 重點(diǎn)中找重點(diǎn)!,Pareto圖分析,Pareto 圖根據(jù) frequency 欄的內(nèi)容判斷各個(gè)缺陷影響的大小，並按從大到小的次序排列。 最後一組總是標(biāo)有 “其他” ，並以默認(rèn)方式包括所有缺陷的分類(lèi)計(jì)算，這幾類(lèi)缺陷非常少， 它們占總?cè)毕莸?5% 以下。 該圖右側(cè) Y 軸表示占總?cè)毕莸陌俜直?，左?cè) Y 軸表示缺陷數(shù)。 紅線 (在螢?zāi)簧峡梢钥吹? 表示累積百分比，而直方圖表示每類(lèi)缺陷的頻率 (占總量的百分比) 。在圖的下方列出所有

31、的值,百分比,缺陷的Pareto圖,計(jì)數(shù),缺陷 計(jì)數(shù) 274 59 43 19 10 18 百分比 64.8 13.9 10.2 4.5 2.4 4.3 累積百分比 64.8 78.7 88.9 93.4 93.4 100.0,螺釘丟失,夾子丟失,襯墊泄漏,外殼有缺陷,零件不完整,其他,400 300 200 100 0,100 80 60 40 20 0,百分比（%）,品質(zhì)統(tǒng)計(jì)圖表 -柏拉圖(Pareto Diagrams),層別Pareto圖: 解釋分組資料,上圖使用了一個(gè) By Variable（從屬變數(shù)），所有的圖都在一頁(yè)上。 下圖使用同樣的命令，沒(méi)有從屬變數(shù)。 當(dāng)選擇每頁(yè)一張圖時(shí)，所

32、有的圖的計(jì)數(shù)(左軸)刻度相同。 右側(cè)的百分比只反映該圖占總體的百分比。 這些圖表明， 70%的記錄缺陷是刮傷和剝落的 (下部)，約有一半的缺陷是夜班人員記錄的 (上右圖)。 此外，記錄缺陷是刮傷和剝落的比例，對(duì)白班和夜班的 來(lái)說(shuō)似乎也差不多。然而，晚班和周末班出現(xiàn)的缺陷樣式是不同的。,裂紋Pareto圖,白班,晚班,夜班,周末班,刮傷 剝落 其他 污點(diǎn),15 10 5 0,15 10 5 0,15 10 5 0,15 10 5 0,裂紋Pareto圖,40 30 20 10 0,100 80 60 40 20 0,缺陷 計(jì)數(shù) 15 13 6 6 百分比 37.5 32.5 15.0 15.0

33、累積百分比 35.5 70.0 85.0 100.0,刮傷,撥落,其他,污點(diǎn),計(jì)數(shù),計(jì)數(shù),計(jì)數(shù),計(jì)數(shù),計(jì)數(shù),百分比（%）,品質(zhì)統(tǒng)計(jì)圖表 -柏拉圖(Pareto Diagrams),品質(zhì)統(tǒng)計(jì)圖表 -散佈圖(Scatterplots),Until now, all the graphical tools weve discussed have been for examining the distribution of a single process characteristic. The scatterplot is a graphical tool for examining the rel

34、ationship between two process characteristics. A scatterplot is an X-Y plot of one variable versus another. Each unit of product usually has many characteristics, process input variables, etc. One objective might be to see whether two variables or characteristics are related to each other (i.e., to

35、see what happens to one of the variables when the other variable changes). This relationship between two variables is called correlation. Scatterplots can help us answer this type of question.,品質(zhì)統(tǒng)計(jì)圖表 -散佈圖(Scatterplots),品質(zhì)統(tǒng)計(jì)圖表 -散佈圖(Scatterplots),In addition to telling us whether or not two variables

36、are related, scatterplots can tell us how they are related, and the strength of the relationship:,Strong Positive Correlation 強(qiáng)正相關(guān),No Correlation無(wú)關(guān),Weak Negative Correlation 弱負(fù)相關(guān),Weak Positive Correlation 弱正相關(guān),Strong Negative Correlation 強(qiáng)負(fù)相關(guān),品質(zhì)統(tǒng)計(jì)圖表 -散佈圖(Scatterplots),In addition, scatterplots are a

37、n excellent tool for determining the type of relationship between the two variables, as well as looking for outliers:,Linear Relationship 線性相關(guān),Outliers 特異,Non-Linear Relationship 非線性相關(guān),品質(zhì)統(tǒng)計(jì)圖表 -散佈圖(Scatterplots),Correlation and Causation We must always take care not to confuse correlation with causat

38、ion. The fact that two characteristics are correlated does not prove that one causes the other. Both may be related to some other factor which is the true root cause.,But is there a cause-effect relationship between the two? Did the increase in TVs cause the number of accidents to go up? (Not likely

39、.) Did the increase in traffic accidents cause people to buy more TVs? (Not likely, either.),品質(zhì)統(tǒng)計(jì)圖表 -趨勢(shì)圖(Trend Charts),Trend Charts Stability: A process is stable if its mean and standard deviation are constant and predictable over time. A disadvantage of histograms and normal probability plots is t

40、hat they cannot be used to determine whether the process is stable over time. A plot of the data in time order will allow us to do that. These time-ordered plots, called Trend charts and Control charts are essential when examining the stability of a distribution over time. A trend chart or a control

41、 chart can detect instability if it exists. Control charts, which are a special kind of trend chart, are discussed in detail separately in a later course module. 可看出穩(wěn)定性及預(yù)測(cè)性,品質(zhì)統(tǒng)計(jì)圖表 -趨勢(shì)圖(Trend Charts),The table below contains average plating thickness measurements taken from 21 lots of product. Below

42、that is a trend chart of the data.,品質(zhì)統(tǒng)計(jì)圖表 - Noisy,The results of a statistical analysis can be seriously affected by the failure of the data to meet certain required assumptions. One of the most common assumptions is that the data values are independent and that they come from a Normal distribution.

43、 This assumption can be violated in several ways: Outliers (points that do not fit the rest of the distribution) in the data, Non-Normal-shaped distributions (multi-modal or skewed distributions), Data that exhibit these characteristics can be thought of as noisy data. The procedures in this section

44、 provide techniques for effective detection and analysis of noisy data.,雜訊,品質(zhì)統(tǒng)計(jì)圖表 - Noisy,Boxplots,Trend Chart,Histogram,Scatterplot,Normal Prob. Plot,品質(zhì)統(tǒng)計(jì)圖表 - Noisy,Recommended strategy for handling outliers: 1. Identify the outliers using the methods described in the following pages. If possible,

45、find the causes of the outliers. Remove the outliers with identified causes from the data set(找原因). 2. If all the outliers can be explained, then analyze the data as usual. 3. However, if there are any outliers that do not have explanations, analyze the data twice: including the outliers, excluding

46、the outliers. See if and how the analysis results differ.,製程能力分析與SPC統(tǒng)計(jì)製程控制,當(dāng)製程開(kāi)始產(chǎn)生變異時(shí),其統(tǒng)計(jì)分佈圖的形狀也開(kāi)始變化。通常變化不外下面三種基本狀況的組合:,若將每日之統(tǒng)計(jì)分佈串起來(lái)一起看,則又可看到更多變異現(xiàn)象,一般可分為兩種如下:,時(shí)間,時(shí)間,1.突發(fā)變異:製程中有特殊或突發(fā)原因而產(chǎn)生變異, 造成不穩(wěn)定。例:每日生產(chǎn)參數(shù)設(shè)定漂移。,2.共同變異:製程中只有共同原因的變異 此種現(xiàn)象是穩(wěn)定的”不良”。例:模具尺寸超差。,瞭解以上基本觀念後便開(kāi)始加入管制的觀念。作管制時(shí)加入規(guī)格上下線, 超出規(guī)格則視為不良如下圖:,

47、製程能力不好,中心值不在目標(biāo),分佈雖集中但超出規(guī)格外,製程能力最差,中心值不在目標(biāo),分佈不集中且超出規(guī)格外,計(jì)算Ca,Cp,Cpk公式,規(guī)格中心m,LSL,+ 3 ,- 3 ,製程寬度6 ,規(guī)格寬度T,USL,Su,SL,Ca: Capability of Accuracy準(zhǔn)確度:,實(shí)際中心,Ca只對(duì)雙邊規(guī)格適用. 分級(jí)標(biāo)準(zhǔn)如下:,主值,計(jì)算Ca,Cp,Cpk公式,規(guī)格中心m,LSL,+ 3 ,- 3 ,製程寬度6 ,規(guī)格寬度T,USL,Su,SL,Cp: Capability of Precision精確度:,實(shí)際中心,當(dāng)僅有下限時(shí):Cp = ( -SL)/(3),對(duì)雙邊規(guī)格: Cp = T

48、/(6),當(dāng)僅有上限時(shí): Cp = (Su- )/(3),分級(jí)標(biāo)準(zhǔn)如下:,計(jì)算Ca,Cp,Cpk公式,Cpk: 指制程能力參數(shù), 是Cp和Ca的綜合. 對(duì)雙邊規(guī)格: Cpk=(1-Ca)*Cp= Min(Su- )/(3), ( -SL)/(3) 對(duì)單邊規(guī)格, 可以認(rèn)為T(mén)為, 則 Ca= ( -)/ (T/2)= 0 Cpk= (1-Ca)*Cp= Cp,分級(jí)標(biāo)準(zhǔn)如下:,SPC介紹,SPC是用於研究變動(dòng)的一種基本工具,它使用統(tǒng)計(jì)信號(hào)監(jiān)測(cè)並改善過(guò)程績(jī)效。該工具可用於任何領(lǐng)域：製造業(yè)、商業(yè)，銷(xiāo)售業(yè)等等 SPC是統(tǒng)計(jì)程式控制（ Statistical Process Control）的縮寫(xiě)。大多數(shù)公

49、司是將 SPC用於最終産品 (Y)上, 而不是用於過(guò)程特徵 (X)。 第一步是使用統(tǒng)計(jì)方法控制公司的輸出。然而，只有我們將重點(diǎn)放在控制輸入 (X),而不是控制輸出 (Y)時(shí), 我們才能認(rèn)識(shí)到我們?cè)谔岣哔|(zhì)量、生産率及降低成本上的努力收效有多大。,什麼是統(tǒng)計(jì)製程控制（SPC）,所有過(guò)程都有固有變動(dòng)（由於一般原因）和非固有變動(dòng)（由於特殊原因）， 我們使用SPC來(lái)監(jiān)測(cè)並改善過(guò)程。 SPC的使用使我們能夠通過(guò)失控信號(hào)發(fā)現(xiàn)特殊原因。這些失控信號(hào)無(wú)法說(shuō)明過(guò)程失控的原因，只能表明過(guò)程處?kù)妒Э貭顟B(tài)。 控制圖表是在統(tǒng)計(jì)上從時(shí)間上跟蹤過(guò)程和産品參數(shù)的方法?？刂茍D表中包括反映過(guò)程隨機(jī)變動(dòng)固有限值的上下控制限值。 這些

50、限值不應(yīng)與 顧客規(guī)定限值相比較 。,什麼是統(tǒng)計(jì)製程控制（續(xù)）,基本統(tǒng)計(jì)原理，控制圖表能夠用於識(shí)別過(guò)程變數(shù)中的非固有（非隨機(jī)）型式。當(dāng)控制圖表出現(xiàn)非隨機(jī)型式信號(hào)時(shí)，我們就可以知道特殊原因引起的變動(dòng)改變了過(guò)程。我們採(cǎi)用措施修正控制圖表中非隨機(jī)型式，這是成功使用 SPC的關(guān)鍵。 控制限值是以爲(wèi)衡量的Y或X建立 3限值爲(wèi)基礎(chǔ)。,過(guò)程改善及控制圖,過(guò)程,衡量系統(tǒng),輸入,輸出,1. 發(fā)現(xiàn)可指定的原因,4. 驗(yàn)證結(jié)果,3.實(shí)施修正措施,2. 確定根本原因,控制圖的益處,用於提高生産率的已證實(shí)的技術(shù) 有效防範(fàn)缺陷 防止不必要的過(guò)程調(diào)整 提供診斷資訊 提供關(guān)於過(guò)程能力的資訊,控制圖類(lèi)型,控制圖有許多類(lèi)型，但是它

51、們的根本原理是相同的 利用 SPC和過(guò)程目標(biāo)方面的知識(shí)選擇正確的類(lèi)型 根據(jù)以下幾方面選擇控制圖類(lèi)型： 資料類(lèi)型: 屬性還是變數(shù)? 採(cǎi)樣容易：樣本同質(zhì)性 資料分佈: 正?；蚍钦? 分組大小: 不變的或變化的? 其他考慮,控制圖的組成,KVOP的X均值圖,2,0,1,0,0,6,1,5,6,0,5,5,9,5,5,8,5,樣本數(shù),X,=,5,9,9,.,1,U,C,L,=,6,1,3,.,6,L,C,L,=,5,8,4,.,6,控制下限,UCL = m +ks 中線 = m LCL = m - k s,其中 m = 樣本均值 s = 樣本標(biāo)準(zhǔn)偏差 k = 控制限制距中線的差值 (通常爲(wèi) 3),記

52、住: 控制限值與顧客規(guī)定限值無(wú)關(guān),控制上限,中線,樣本均值,常用控制圖類(lèi)型(X-S),常用控制圖類(lèi)型(X-R),短期N 30,For control charts with N 30 lots, rather than the usual UCL (upper control limit) and LCL (lower control limit), there are dual sets of control limits: Outer Control Limits(3s). Inner Control Limits (1s).,短期N 30,Any point outside either

53、 of the outer control limits indicates an unstable process.,All points falling between both inner control limits indicates a stable process.,If any points fall inside either “uncertainty zone” (but none are outside the outer control limits), we cannot say whether or not the process is stable, because we do not yet have enough lots to be sure at this time.,With few lots, the control chart has wide uncertainty zones. It is p